where polynomials By Joanna Gutt Lehr Pinnacle Learning Lab last updated 12010 VERTICAL ASYMPTOTE S x c A v ertical asymptote ID: 473735
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ASYMPTOTES OF RATIONAL FUNCTIONS where polynomials. ___ _____________ ________ __________________________________ By Joanna Gutt - Lehr, Pinnacle Learning Lab, last updated 1/2010 VERTICAL ASYMPTOTE S , x = c A v ertical asymptote is a v ertical line that guides the graph of the function but is not part of it. It can never be crossed by the graph because it occur s at the x - value that is not in the domain of the function. A function may have more than one vertical asymptote. To find the eq uations of vertical asymptotes do the following: 1. Reduce the function to the lowest terms if possible, i.e. factor the numerator, N(x) , and the denominator, D(x ) , and cancel all common factors. (This is done to avoid confusing holes with vertical asymptotes.) 2. S et the denominator of the reduced function to zero and s olve . If x = c is a real zero of the denominator then x = c is an equation of a vertical asymptote. Examples - f is written in lowest terms . h is not in lowest terms so reduce: - Denominator x – 2 = 0 produces a v ertical asymptote x = 2. - g is not in lowest terms so reduce the common factors. Since the factor (x – 2) reduced c ompletely, there is a hole in t he g raph at the point where x = 2, i.e. at (2, 6)